The Smallest Harmonic Index of Trees with Given Maximum Degree
The harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Zielona Góra
2018-05-01
|
| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2019 |
| _version_ | 1797718002162991104 |
|---|---|
| author | Rasi Reza Sheikholeslami Seyed Mahmoud |
| author_facet | Rasi Reza Sheikholeslami Seyed Mahmoud |
| author_sort | Rasi Reza |
| collection | DOAJ |
| description | The harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T. |
| first_indexed | 2024-03-12T08:44:38Z |
| format | Article |
| id | doaj.art-2d1835e4f29b4eaeae14bf23e05c00ac |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T08:44:38Z |
| publishDate | 2018-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-2d1835e4f29b4eaeae14bf23e05c00ac2023-09-02T16:29:33ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922018-05-0138249951310.7151/dmgt.2019dmgt.2019The Smallest Harmonic Index of Trees with Given Maximum DegreeRasi Reza0Sheikholeslami Seyed Mahmoud1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. IranDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. IranThe harmonic index of a graph G, denoted by H(G), is defined as the sum of weights 2/[d(u) + d(v)] over all edges uv of G, where d(u) denotes the degree of a vertex u. In this paper we establish a lower bound on the harmonic index of a tree T.https://doi.org/10.7151/dmgt.2019harmonic indextrees05c1292e10 |
| spellingShingle | Rasi Reza Sheikholeslami Seyed Mahmoud The Smallest Harmonic Index of Trees with Given Maximum Degree Discussiones Mathematicae Graph Theory harmonic index trees 05c12 92e10 |
| title | The Smallest Harmonic Index of Trees with Given Maximum Degree |
| title_full | The Smallest Harmonic Index of Trees with Given Maximum Degree |
| title_fullStr | The Smallest Harmonic Index of Trees with Given Maximum Degree |
| title_full_unstemmed | The Smallest Harmonic Index of Trees with Given Maximum Degree |
| title_short | The Smallest Harmonic Index of Trees with Given Maximum Degree |
| title_sort | smallest harmonic index of trees with given maximum degree |
| topic | harmonic index trees 05c12 92e10 |
| url | https://doi.org/10.7151/dmgt.2019 |
| work_keys_str_mv | AT rasireza thesmallestharmonicindexoftreeswithgivenmaximumdegree AT sheikholeslamiseyedmahmoud thesmallestharmonicindexoftreeswithgivenmaximumdegree AT rasireza smallestharmonicindexoftreeswithgivenmaximumdegree AT sheikholeslamiseyedmahmoud smallestharmonicindexoftreeswithgivenmaximumdegree |